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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A statistical study is an analysis of data gathered from a specific group, or population,

to answer a question concerning the group. This is done by gathering various types of data:

- responses from interviews
- observations
- measurements
- counts

Statistical studies follow a standard general process.

When the population is large, it is often impractical to collect data from all test subjects. Thus, data can be obtained from a subgroup, or sample, of the population. If the sample maintains the demographics of the population, it isWhen taking a sample of a population, it is necessary to select the individuals or objects from which the data is collected. The sample should represent the population as a whole so it can be said that the results apply to the population. Therefore, the selection of the sample is important. Often, this means making a random selection, in which chance determines which parts of the population are included in the sample.

If the population is divided into different sub-groups that share similar characteristics, the selection should be made to reflect this distribution. This is known as a *stratified sample.* For example, if the population contains $80%$ men and $20%$ of women, then the sample should also have four times as many men as women.

If a sample is taken that doesn't accurately represent the population, the data collected in the study will likely be unreliable. An error that occurs when making an incorrect sampling is called

Two different samples are described below. Determine if it's a random sample or if it's biased.

- The CEO of a company wants to know what the employees think of their working hours. She asks the employees to fill out a form.
- Every third player in a women's football team is interviewed about the quality of their training equipment.

Show Solution

If a sample represents the population as a whole, the sample is said to be representative. If not, there is an error in the sampling called bias. Therefore, we should determine if each sample represents the population or not.

- Since the employees are asked to fill out the form, they can choose to do so. Thus, it's possible that most people with a strong opinion about their working hours will participate. We can not be certain that the participants represent the whole population. Therefore, the sample is
**biased**. - Since every third player is interviewed there is no specific group in the population that is chosen. Therefore, it's a
**random**sample and its representative of the whole population.

A hypothesis is an assumption regarding a parameter in a population. Here are two examples.

- Smokers have a shorter life expectancy than non-smokers.
- The medication Migraine Away is more effective against migraine than any other treatment.

There are several different methods to collect data for statistical studies. Often, which method is best depends on the purpose of the study.

A survey is when one or more characteristics of a population is studied by collecting data from every member of the sample. The data can be obtained by asking questions or making measurements.

An experiment involves a group of participants undergoing a specific treatment with the goal of collecting data about their reactions to the treatment.

In some statistical studies it is necessary to conduct an experiment in order to collect the data. For example, this method is often used when studying the effects of a medical treatment.

Determine the type of statistical study.

- You want to determine what percent of customers in a local grocery store buys cheese. Data is collected by standing outside the store and asking the customers questions as they exit.
- A team of researchers test a new vaccine against measles on $100$ students who volunteered to participate.
- A referendum in Belmar, New Jersey, on whether it should be compulsory for the shop owners in town to have a porcelain cat in the shop window.
- Professor Potocoff conducts a study to determine if patients who are treated for high blood pressure have an increased risk of getting malaria. She does the study by analyzing information in a database at the hospital where she works.

Show Solution

- Here, one characteristic of a population is studied and every member of the sample is asked the same question. Therefore, it is a survey.
- Here, the participants undergo a treatment — the vaccine. Thus, it is an experiment.
- In a referendum, everyone in the population is asked the same question. Thus, it is a survey.
- The professor gathers data from a database; she does not interact with the participants. As there is no treatment conducted, it is an observational study.

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